1. Field of the Invention
The present invention generally relates to tool control system and solves the problem of mis-processing wafer lots/wafers by monitoring specific physical parameters of the tool set in real time. These parameters include any measurable quantifications relating to the process or tool, such as gas flow, temperature, pressure, power, etc.
2. Description of Related Art
A manufacturing line is generally controlled using three logistic functions: lots must be routed to the proper tool set; recipes for various process steps must be routed to an individual process tool; and wafer lots must be matched to tool and then to a recipe. Further, two control functions exist. The first control function is to track the logistics functions. The second is to control the process tool parameters (e.g., to decide when a tool malfunction or tool fault has occurred.)
The tool process parameters form a multivariate data set. The monitoring of such datasets has been the subject of many works, some of which are mentioned below. The set of tool data to be analyzed is very large and can be considered a three-dimensional dataset.
The first dimension of the three-dimensional dataset is the process parameter. Examples of process parameters include chamber pressure, temperature, gas flows, and RF power. The second dimension is time, with data for each process parameter being taken at regular times during wafer processing. The third dimension is the batching of data as defined by wafer.
Thus, the dataset consists of a time series for each process parameter, for each wafer processed. To reduce this dataset to a few indicators of tool performance (or health), i.e., a few surrogate variables, a data reduction scheme is necessary.
Nomikos (P. Nomikos and J. F. MacGregor, xe2x80x9cMultivariate SPC Charts for Monitoring Batch Processes,xe2x80x9d Technometrics, vol. 37, No. 1, pp. 41-59, February 1995), incorporated herein by reference, discuss one such scheme by rearranging the three-dimensional dataset into a two-dimensional matrix and then performing a conventional principal components analysis (PCA). Spanos C. J. Spanos, H. F. Guo, A. Miller and J. Leville-Parrill, xe2x80x9cReal-Time Statistical Process Control Using Tool Data,xe2x80x9d IEEE Trans. on Semicond. Manuf, vol. 5, No. 4, pp. 308-318, November 1992, incorporated herein by reference, describes a method to process time series (without regard to batching by wafer) using a time series filter. The Spanos article then describes using a Hotelling T2 function to reduce groupings of n time series points to a single surrogate variable.
Lee (S. F. Lee, E. D. Boskin, H. C. Liu, E. H. Wen and C. J. Spanos, xe2x80x9cRTSPC: A Software Utility for Real-Time SPC and Tool Data Analysis,xe2x80x9d IEEE Trans. on Semicond. Manuf, vol. 8, No. 1, pp. 17-25, February 1995), incorporated herein by reference, describes a second method to reduce the dataset by collapsing the time series for each wafer using the average value of the time series, or the length of the time series (i.e., the process step). U.S. Pat. No. 5,442,562, incorporated herein by reference, describes a general method of reducing a plurality of process intermediate process variables (such as principal components) to a single surrogate variable, determining which intermediate variable is outside a predetermined limit, determining which process variable is the primary contributor and then correcting that process variable automatically via a computer.
When a two-dimensional dataset is to be monitored, for example, tool parameters such as pressure, gas flow, or temperature vs. wafer identity are to be monitored, a statistic called the Hotelling Function (T2) can be used (see for example Doganaksoy, (N. Doganaksoy, F. W. Faltin and W. T. Tucker (1991)), xe2x80x9cIdentification of Out of Control Quality Characteristics in a Multivariate Manufacturing Environment,xe2x80x9d Comm. Statist.xe2x80x94Theory Meth., 20, 9, pp. 2775-2790), incorporated herein by reference, where:       T    2    =                              (                                    n              ref                        ⁢                          n              new                                )                ⁢                  (                                    n              ref                        -            p                    )                                      (                                    n              ref                        ⁢                          n              new                                )                +                              (                                          n                ref                            -              1                        )                    ⁢          p                      ⁢                  (                  x          -                      x            _                          )            T        ⁢                  S                  -          1                    ⁢              (                  x          -                      x            _                          )            
where x=vector of measured values, {overscore (x)}=vector of reference means (based on history), and Sxe2x88x921 is the inverse covariance matrix (based on history), nref is the size of the reference sample, nnew is the size of the new sample and p is the number of variables. This function obeys an F statistic, F(p, nref-p,alpha). Where alpha is the probability corresponding to a desired false call rate (presuming the distributions of the individual parameters are normal).
Another related technique for reducing a two-dimensional dataset to a surrogate variable is known as principal component analysis (PCA) which is incorporated by Jackson (J. Edward Jackson, A User""s Guide to Principal Components, John Wiley and Sons, Inc. (1991) M. J. R. Healy, Matrices for Statistics, Oxford Science Publications (1986)), incorporated herein by reference. In this method, the eigenvectors of the covariance matrix (or alternately the eigenvectors of the correlation matrix) form a set of independent intermediate variables, consisting of linear combinations of the original process variables. These principal components may be monitored separately, by taking only the most significant or by monitoring the residuals. Alternatively, the principal components may be monitored in aggregate, in which case the sum of squares distance of a particular sample from its principal components is identical to the Hotelling T2 surrogate variable.
One difficulty with multivariate methods is that, once an out-of-control situation is detected, determining which process variables caused the problem is difficult, based on a single or few indicator variables. This is often known as the T2 decomposition problem. Doganaksoy, above, provides a method to solve the decomposition problem, that orders the process variables in order of descending normalized difference from their means, i.e., (xixe2x88x92{overscore (x)}i)/"sgr"i, the univariate statistic.
Runger (G. C. Runger, F. B. Alt, xe2x80x9cContributors to a multivariate statistical Process control chart signal,xe2x80x9d Commun. Statist.xe2x80x94Theory Meth. 25(10) 2203-2213 (1996)), incorporated herein by reference, provides another such method by considering the change in the T2 score if the process parameter is not included (the xe2x80x9cdrop 1xe2x80x9d T2 score, aDi).
However, the conventional systems are not adequately able to distinguish between variations that do not affect products and variations that do affect products. The invention solves this and other problems of the conventional systems, as discussed below.
It is, therefore, an object of the present invention to provide a structure and method for controlling a manufacturing tool, including measuring different manufacturing parameters of the tool, transforming a plurality of time series of the manufacturing parameters into intermediate variables based on restrictions and historical reference statistics, generating a surrogate variable based on the intermediate variables, if the surrogate variable exceeds a predetermined limit, identifying a first intermediate variable, of the intermediate variables, that caused the surrogate variable to exceed the predetermined limit and identifying a first manufacturing parameter associated with the first intermediate variable, and inhibiting further operation of the tool until the first manufacturing parameter has been modified to bring the surrogate value within the predetermined limit.
The surrogate variable comprises T2, where:             T      2        =                                        (                                          (                                  x                  -                                      x                    _                                                  )                            σ                        )                    T                ⁢                              R                          -              1                                ⁢                      (                                          (                                  x                  -                                      x                    _                                                  )                            σ                        )                              =                        z          T                ⁢                  R                      -            1                          ⁢        z              ,
where x comprises the intermediate variables, {overscore (x)} comprises a historical sensor value, "sgr" comprises a historical standard deviation sensor value, Rxe2x88x921 comprises an inverse correlation matrix, z comprises mean and standard deviation normalized values. Further, x and "sgr" are user-adjustable which provides a substantial advantage over conventional systems.
The transforming reduces the dimensionality of the time series of the manufacturing parameters. Also, the transforming includes one or more of selecting, modifying and combining the time series of the manufacturing parameters based on the restrictions and the historical reference statistics. Further, the data may be pre-processed to normalize all of the incoming time series. The restrictions comprise user-defined, batch-specific restrictions.
Another embodiment of the invention is a computer implemented method of controlling a tool using multivariate analysis that includes measuring a set of tool variables with sensors, storing values of the variables in a computer connected to receive data from the sensors (the computer generating a surrogate variable having a value representative of whether the tool is in control, the surrogate variable being a function of a plurality of intermediate variables), determining if the value of the surrogate variable is outside of a predetermined limit (the computer identifying an out-of-control intermediate variable of the intermediate variables that primarily contributed to the value of the surrogate variable), identifying an out-of-control tool variable of the tool variables that primarily contributed to the out-of-control intermediate variable, and inhibiting further operation of the tool until the out-of-control tool variable has been modified to bring the surrogate value within the predetermined limit.
The inventive method also includes inputting reference statistics and a transformation program into the computer; inputting raw data from process runs into the computer; using the transformation program to compute the intermediate variables from the raw data; and applying the reference statistics to a scaled version of a Hotelling function and computing the T2 score for the surrogate variable based on the intermediate variables.
A further embodiment of the invention is a computerized method of determining corrections for a manufacturing process that includes measuring a set of manufacturing parameters, performing a first T2 score computation using the manufacturing parameters, providing a first inverse matrix using intermediate variables obtained from the first T2 score computation, using the first inverse matrix to create a generalized formulation for such matrices, using the generalized formulation to compute a second T2 score for the inverse matrix with one variable missing, and subtracting the second T2 score from the first T2 score. The invention also includes repeating the computing and the subtracting for each of the intermediate variables; and ranking results of the subtracting to identify an out-of-control intermediate variable.
The invention also includes a computer interface for creating a file for transformation of various process recipes, process tools and products in a statistical analysis of a manufacturing process. The computer interface includes an input device for inputting data, a correction device for correcting missing data in a time series of the data by determining a length of the times series and an interpolation interval of the time series, a first selector for selecting a transformation function, a generator for generating one or more control charts from a Hotelling function using the data corrected by the correction device and using the transformation function, and a second selector for selecting between the control charts. The Hotelling function comprises T2, where:             T      2        =                                        (                                          (                                  x                  -                                      x                    _                                                  )                            σ                        )                    T                ⁢                              R                          -              1                                ⁢                      (                                          (                                  x                  -                                      x                    _                                                  )                            σ                        )                              =                        z          T                ⁢                  R                      -            1                          ⁢        z              ,
where x comprises the intermediate variables, {overscore (x)} comprises a historical sensor value, "sgr" comprises a historical standard deviation sensor value, Rxe2x88x921 comprises an inverse correlation matrix and z comprises mean and standard deviation normalized values. Further, the transformation function reduces a dimensionality of the time series of the manufacturing parameters. The transformation function selects, modifies and combines the time series of the manufacturing parameters based on restrictions and historical reference statistics, where the restrictions comprise user-defined, batch-specific restrictions.
Thus, the invention collapses the three-dimensional dataset to two-dimensions in an automated way, while still providing a convenient means to include human expertise. Once this two-dimensional dataset is determined, more conventional multivariate reduction methods such as Hotelling T2 and PCA can be used further to reduce data to a few surrogate variables.
To incorporate human expertise, the invention includes a human configurable transformation programming language that selects a set of process variable time series, performs vector-to-vector operations (to produce a new set of time series), and performs vector-to-scalar operations on the new time series to obtain a one-dimensional set of scalar xe2x80x9cintermediatexe2x80x9d variables for each item processed.
The inventive system determines if a parameter shift will put products at risk based on historical reference data and codified human expertise. When a significant change occurs, the system identifies the tool, the most likely parameters, and suggests corrective action. The invention inhibits use of the tool until corrective action is taken. The invention also monitors process recipes for changes, authorized or unauthorized.
Further, the present invention provides a practical method for multivariate tool fault detection that prevents wafer mis-processing. The invention uses human expertise to distinguish which variations can be tolerated and which are of interest.